Modelling potential environmental impacts of science activity in Antarctica

Authors
Affiliations

David O’Sullivan

Fraser J. Morgan

Abstract

We use GPS data collected on a science expedition in Antarctica to estimate hiking functions for the speed at which humans traverse terrain differentiated by slope and by ground cover (moraines and rock). We use the estimated hiking functions to build weighted directed graphs as a representation of specific environments in Antarctica. From these we estimate using a variety of graph metrics—particularly betweennness centrality—the relative potential for human environmental impacts arising from scientific activities in those environments. We also suggest a simple approach to planning science expeditions that might allow for reduced impacts in these environments.

1 Introduction

Overview of Antarctic science: when and where, its intensity etc. Background on international treaties, etc.

Relevant findings as to human impacts in Antarctica. Note that in this environment even ‘leave only footprints’ is likely impacting the environment in significant ways.

Overview of sections ahead.

3 Data sources

3.1 Antarctic geospatial data

Geospatial data for Antarctica were obtained from sources referenced in Cox et al. (2023b), Cox et al. (2023a), and Felden et al. (2023). The study area was defined to be the Skelton and Dry Valleys basins, as defined by the NASA Making Earth System Data Records for Use in Research Environments (MEaSUREs) project (Mouginot and University Of California Irvine 2017) and shown in Figure 3 (a). The Skelton basin was included because while the expedition GPS data was ostensibly collected in the McMurdo Dry Valleys, it actually extends into that basin as shown in Figure 3 (b). Elevation data from the Reference Elevation Model of Antarctica project Howat et al. (2022), and geology from GeoMAP Cox et al. (2023b) are shown in Figure 3 (c). The five largest areas of contiguous non-ice surface geology across the study area shown in Figure 3 (d) were chosen to be the specific sites for more detailed exploration using the methods set out in this paper. These range in size from around 320 to 2600 square kilometres.

(a) Study area location in Antarctica

 

(b) Skelton and Dry Valleys basins
(c) Study area elevation (hillshade) and surface geology

 

(d) Five sub-regions of contiguous surface geology
Figure 3: The study area.

3.2 GPS data from an expedition

FRASER: Timeline, devices used, and associated protocols for scientists while on site.

GPS data were processed to make them better suited for use in the estimation of hiking functions.

The first processing step was to confirm the plausibility of the data, particularly the device-generated speed distance between fixes, and elevations associated with fixes. The challenges of post-processing GPS data are well documented and relate to issues with GPS drift which can lead to estimated non-zero movement speeds as a result of noise in the signal. The raw GPS data included distance since last fix, speed, and elevation estimates and it was determined in all cases that the device generated results for these measurements were likely to be more reliable than post-processing the raw latitude-longitude fixes to calculate the values.

The second processing step was to remove fixes associated with faster movement on other modes of transport than walking. Wood et al. (2023) cite a number of previous works that base detection of trip segments based on recorded speeds. This method was trivially applicable to our data to a limited degree as scientists arrive at the expedition base camp and occasionally also travel on helicopters on trips to more remote experimental sites.

The third, more challenging processing step was to deal with sequences of fixes associated with non-purposeful movement when scientists were in or around base camp, at rest stops, or at experimental sites. Crude filters removed fixes with low recorded distances between fixes (less than 2.5 metres), high turn angles at the fix location (greater than 150°), and fixes recorded on ice-covered terrain, but this didi not clean the data sufficiently for further analysis. An additional filtering step was to count fixes (across all scientists) in square grid cells and remove all fixes in grid cells with more than 50 fixes.

This left one persistent concern: an over-representation of consecutive fixes recorded at exactly the same elevation, resulting in many fixes with estimated slopes of exactly 0, and leading to a clearly evident dip in estimated movement speeds at 0 slope (Figure 4 (a)). It is likely that these fixes are associated with GPS device drift, so a it was decided to remove all fixes where estimated slope was exactly 0. Figure 4 (b) shows the improvement in even a crudely estimated hiking function derived from local scatterplot (LOESS) smoothing. Note that such functions are likely overfitted and not used further in our analysis where we favour more easily parameterised functions such as those discussed in Section 2.1.

(a) Boxplots by slope of speed, with smoothed estimated hiking function showing a ‘dip’ due to over-representation of 0 slope fixes

 

(b) After filtering the estimated hiking function no longer has a dip.
Figure 4: GPS data and crudely estimated hiking functions before and after filtering the to remove fixes associated iwht non-purposive movement.

4 Methods and results

4.1 Hiking functions

We fit three alternative functional forms to the cleaned GPS data: exponential (Tobler 1993), Gaussian (following Irmischer and Clarke 2018), and Lorentz (following Campbell et al. 2019) using the Levenburg-Marquardt algorithm (Moré 1978) as provided by the nlsLM function in the minpack.lm R package (Elzhov et al. 2022). The raw data and fitted curves are shown in Figure 5.

Figure 5: Three possible hiking functions applied to GPS data split by land cover.

The Lorentz function offers a marginal improvement in the model fit in comparison with the Gaussian function, while both are clearly better than the exponential form. However, the improvement offered by the Lorentz function over the Gaussian is marginal: residual standard error 1.489 vs 1.491 on Moraine, and 1.487 vs 1.488 on Rock, and inspection of the curves shows that estimated hiking speeds for the Gaussian functions are much closer to a plausible zero on very steep slopes. We therefore chose to adopt Gaussian hiking functions for the remainder of the present work.

In previous work researchers have applied a ground cover penalty cost to a base hiking function to estimate traversal times. We instead, as shown, estimate different hiking functions for the two ground cover types present. The peak speed on rock is attained on steeper downhill slopes than on moraines, perhaps indicative of the greater care required on downhill gravel slopes. Meanwhile the highest speeds on level terrain are attained on moraines.

Overplotting of the hiking functions including an additional model fitted to all the data, confirms that the fitted functions are sufficiently different to retain separate models for each ground cover (see Figure 6). Plotting both functions in the same graph makes clearer the difference in maximum speed and slope at maximum speed associated with each ground cover.

Figure 6: The hiking functions for All, Moraine and Rock ground covers compared, including 95% confidence intervals derived by Monte-Carlo simulation.

4.2 Landscapes as graphs

We developed R code (R Core Team 2024) to build graphs (i.e. networks) with hexagonal lattice structure and estimated traversal times for graph edges derived from our hiking functions. Graphs are stored as igraph package (Csárdi and Nepusz 2006; Csárdi et al. 2024) graph objects for further analysis.

How terrain is handled in graph edge cost estimation (i.e., assigning half the cost from the terrain at the vertex at each end of the edge).

igraph implements betweenness centrality measures (Freeman 1978; Brandes 2001), which we used to identify vertices and/or edges most likely to be traversed by minimum travel time routes across the terrain.

4.3 Betweenness centrality limited by radius.

4.4 Impact minimizing networks

Tentative proposal for impact minimizing networks based on minimum spanning trees, but noting the issue with respect to directed graphs when these would more correctly be arborescences (Korte and Vygen 2018).

5 Discussion

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6 Conclusions

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